ArcTan comes in two flavors
ArcTan[z]
and
ArcTan[x,y]
When x>0 and y>0
ArcTan[x,y]
can be simplified to
ArcTan[y/x]
How can I tell Mathematica that this is what I want?
If you give ArcTan integer values it looks like it automatically does this. If you just give it variables x and y it doesn’t do this by default. But you can use replacement with a rule to do this.
In[1]:= ArcTan[3, 7]
Out[1]= ArcTan[7/3]
In[2]:= ArcTan[x, y]
Out[2]= ArcTan[x, y]
In[3]:= ArcTan[x, y] /. ArcTan[x_, y_] -> ArcTan[y/x]
Out[3]= ArcTan[y/x]
It looks like you would like this for syntactical purposes of using your own notation. Although, it might make solving some problems easier with simpler relations, plotting and in use of solver functions. Simply define your own function:
c=3
d=4
ArcTan1[y_]=ArcTan[y/c]
ArcTan2[x_]=ArcTan[d/x]
Then you can plot or solve for the values you need relationally on an as needed basis with the appropriate.
If there is a particular application that you have in mind or need a solution for, please add to the discussion.